BIFURCATION IN A PARAMETRICALLY EXCITED TWO-DEGREE-OF-FREEDOM NONLINEAR OSCILLATING SYSTEM WITH 1∶2 INTERNAL RESONANCE  

作　　者：季进臣 陈予恕 

出　　处：《Applied Mathematics and Mechanics(English Edition)》1999年第4期11-20,共10页应用数学和力学（英文版）

摘　　要：The nonlinear response of a two_degree_of_freedom nonlinear oscillating system to parametric excitation is examined for the case of 1∶2 internal resonance and, principal parametric resonance with respect to the lower mode. The method of multiple scales is used to derive four first_order autonomous ordinary differential equations for the modulation of the amplitudes and phases. The steady_state solutions of the modulated equations and their stability are investigated. The trivial solutions lose their stability through pitchfork bifurcation giving rise to coupled mode solutions. The Melnikov method is used to study the global bifurcation behavior, the critical parameter is determined at which the dynamical system possesses a Smale horseshoe type of chaos.The nonlinear response of a two_degree_of_freedom nonlinear oscillating system to parametric excitation is examined for the case of 1∶2 internal resonance and, principal parametric resonance with respect to the lower mode. The method of multiple scales is used to derive four first_order autonomous ordinary differential equations for the modulation of the amplitudes and phases. The steady_state solutions of the modulated equations and their stability are investigated. The trivial solutions lose their stability through pitchfork bifurcation giving rise to coupled mode solutions. The Melnikov method is used to study the global bifurcation behavior, the critical parameter is determined at which the dynamical system possesses a Smale horseshoe type of chaos.

关 键 词：parametric excitation internal resonance Melnikov method 

分 类 号：O322[理学—一般力学与力学基础]